Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the circle area a equals 25 pi centimeters squared and theta equals pi over four

Answer 1

3.928 units.

Explanation:

We know that L, Ф, R are related to each other by the equation

L = RФ, where Ф is in the Radian unit. .... (1)

Now, the area of a circle is given to be πr² =25π, ⇒ r =5 units

And also given that Ф =π/4

Hence, length of the arc (L) =5×
`(\pi )/(4)` =
`(5*22)/(7*4)` =3.928 units. (Answer)